题库搜索>问题求解PS-13196
If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 = 2xn – 1 for n ≥ 1, then x20 – x19 =
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标准做法是等式两边同时减1，得到 xn+1－1 = 2xn – 2＝2(xn -1)
把右边除过去，得到(xn+1－1)/(xn -1)=2说明{xn -1}是等比数列，首项为2，公比为2
所以x20-x19=x19-1＝2*219-1=219
sql
递归啊
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2022-01-17 14:56:43
570852r
算两个出来然后对着答案找规律最快
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2020-12-29 12:35:58
720哥哥
这不是数列吗 怎么被归类到排列组合了
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2019-12-31 17:05:27
187347fa
X1=3，X2=5, X3=9, X4=17, X5=33。。。。，X2-X1=2=2^1， X3-X2=4=2^2, X4-X3=8=2^3, 则X20-X9=2^19
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2019-11-25 20:15:58
cindy710
列出 n=1 x1=3 n=2 x2=5 增加了2 n=3 x3=9 增加了2? 。 。 n=19 x19 增加了2^18 n=20 x20 增加了2^19 x20- x19=增加的部分 2^19
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2019-08-01 16:22:08
cindy710回复cindy710
列出 n=1 x1=3 ; n=2 x2=5 增加了2; n=3 x3=9 增加了2^2; 。 。 ;n=19 x19 增加了2^18; n=20 x20 增加了2^19; ∴ x20- x19=增加的部分 2^19
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2019-08-01 16:23:03
yamm
x1=3=2+1,x2=5=2^2+1,x3=9=2^3+1,所以xn=2^n+1, x20-x19=2^20-2^19=2^19
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2019-02-25 17:16:50
Jiamu
不应该是 2*19次方-1吗。。。
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2018-10-25 21:50:08
苏漾
2*2的18方
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2017-10-13 17:19:52
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